Like @kellyromanych points out, confined spaces help. If we let ours roam around the house, he'd sprinkle all over the place. Once we remembered the trick to close doors and add gates where necessary, basically confining him to one room at a time. And whenever moving out of the confinement (and right after eating, and waking up from sleep) straight outdoors to establish a routine. And praises + treats for doing the right thing, like you would the small puppy. With that, ours soon went to practically house broke. As long as *we* remember to stick to the rules.

Let him familiarize with the house one room at a time, slowly over days and weeks. We thought ours house-broke by now, there hadn't been any "leaks" in two weeks or more, with freedom to move in about half of the house. Then just a couple of days ago, I forgot to close the bedroom door in upstairs. He went off in our bed ‍️ presumably because it was such an exciting place to be all alone, or something to that effect.

He's a little over a year old and was at the humane society for most of his life so far -- I doubt he ever had incentive to "hold it". I take him out and for walks quite frequently and he'll even go on command (very smart and otherwise well-behaved, especially for his age), but once he has any in the tank, he'll just go. Try to keep him in-view at all times, but easier said than done.

Is the dog mat trained?

There is the possibility